Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x + 8$ and $ KL = 6x + 11$ Find $JL$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x + 8} = {6x + 11}$ Solve for $x$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({3}) + 8$ $ KL = 6({3}) + 11$ $ JK = 21 + 8$ $ KL = 18 + 11$ $ JK = 29$ $ KL = 29$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {29} + {29}$ $ JL = 58$